Transmission-Line Resistance Compression Networks And Related Techniques

ABSTRACT

A resistance compression network uses transmission line sections having asymmetric lengths to compress the resistance range of multiple loads. In some embodiments, the characteristic impedance of the transmission line sections is related to the geometric mean of the load resistance range. The resistance compression network may be used within, for example, an energy recovery system or in any other application where a reduction in the resistance range of multiple loads is desired.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 13/800,221, filed on Mar. 13, 2013 which is a continuation of Ser.No. 13/755,335, filed Jan. 31, 2013, which claims the benefit of U.S.Provisional Application No. 61/663,930, filed Jun. 25, 2012, whichapplications are hereby incorporated by reference in their entireties.

FIELD

Subject matter disclosed herein relates generally to radio frequency(RF) systems and, more particularly, to techniques and circuits forshaping the input impedance of one or more load devices in an RF system.

BACKGROUND

In many applications, there is a need to reduce a range over which aninput resistance varies. For example, in an energy recovery system thatuses a plurality of tuned rectifier circuits to convert an RF signal toDC, there may be a need to compress a resistance range looking into thevarious rectifier circuits into a smaller range. The compressedresistance may then be presented to an RF circuit as a resistivetermination. In such applications, a resistance compression network maybe provided to perform the compression. Some examples of resistancecompression networks are described in U.S. Pat. No. 7,535,133 toPerreault et al., which is hereby incorporated by reference herein inits entirety.

As with most circuits and systems, it is generally desirable thatresistance compression networks be relatively simple and inexpensive tofabricate. In addition, it is generally desirable that resistancecompression networks have relatively low loss. It may also be desirablethat such networks be capable of performing other functions in additionto resistance compression. As such, there is a need for resistancecompression networks that are capable of providing some or all of theseattributes.

SUMMARY

Resistance compression networks and techniques are described herein thatuse transmission line segments having asymmetric lengths to reduce arange over which the input resistances of a plurality of loads vary. Theresistance compression networks are capable of being easily andinexpensively fabricated using printed circuit techniques. In addition,the resistance compression networks are capable of lossless or nearlossless operation in some implementations. In some embodiments, theresistance compression networks may be adapted to provide filtrationfunctions in addition to resistance compression. Also, in someembodiments, the resistance compression networks may be adapted toreduce the degree to which an input immittance of a resistancecompression network appears susceptive as compared to the immittance ofa plurality of loads. Multi-stage transmission line resistancecompression networks may be provided in some implementations to generatea higher level of compression. In general, the transmission lineresistance compression networks described herein may provide resistancecompression at a fundamental frequency. In some embodiments, however,transmission line segment lengths may be selected in a manner that alsoprovides compression at one or more harmonic frequencies.

In accordance with one aspect of the concepts, systems, circuits, andtechniques described herein, a resistance compression network isprovided to shape an input impedance at a port for transferring energyto multiple loads at a first frequency. More specifically, theresistance compression network comprises: a first transmission linesegment having a first electrical length at the first frequency, thefirst transmission line segment having an output for coupling to a firstload; a second transmission line segment having a second electricallength at the first frequency, the second electrical length beingdifferent from the first electrical length, the second transmission linesegment having an output for coupling to a second load; and acompression port coupled to inputs of both the first and the secondtransmission line segments; wherein, over a set of operating conditionsof interest, an equivalent resistance looking into the compression portat the first frequency varies over a first resistance range asequivalent resistances of the first and second loads vary over a secondresistance range, wherein a range ratio associated with the firstresistance range is less than a range ratio associated with the secondresistance range, wherein the range ratio of a subject range is a ratioof a largest resistance value in the subject range to a smallestresistance value in the subject range.

In accordance with another aspect of the concepts, systems, circuits,and techniques described herein, a circuit comprises: first and secondloads having substantially the same input impedances under substantiallythe same operating conditions; and a transmission-line resistancecompression network, including: an input port; a first output portcoupled to the first load; a second output port coupled to the secondload; and a transmission-line network coupled to the input port, thefirst output port, and the second output port, the transmission-linenetwork comprising at least two transmission lines of different lengths;wherein, for a first operating range, the resistances at input ports ofthe first and second loads vary over first and second ratios,respectively, the resistance of the input impedance at the input port ofthe transmission-line compression network varies over a third ratio, andthe third ratio is smaller than at least one of the first and secondratios.

In accordance with still another aspect of the concepts, systems,circuits, and techniques described herein, a method is provided forcompressing resistances associated with a plurality of loads. Morespecifically, the method comprises: transforming an input impedance of afirst load using a first transmission line segment having a firstelectrical length at a first frequency, the first load being associatedwith a first resistance range at the first frequency; transforming aninput impedance of a second load using a second transmission linesegment having a second electrical length at the first frequency, thesecond load being associated with a second resistance range at the firstfrequency; and providing a compressed resistance range at a compressionport that is coupled to inputs of the first and second transmission linesegments at the first frequency, the compressed resistance range havinga range ratio that is less than a range ratio associated with at leastone of the first resistance range and the second resistance range,wherein a range ratio of a range comprises a ratio between a highestvalue in the range and a lowest value in the range.

In accordance with a further aspect of the concepts, systems, circuits,and techniques described herein, an energy recovery system to simulatebehavior of a resistive termination for a radio frequency (RF) circuitcoupled to the energy recovery system is provided. More specifically,the energy recovery system comprises: a rectification system having aplurality of tuned rectifier circuits, the plurality of tuned rectifiercircuits including at least a first tuned rectifier circuit and a secondtuned rectifier circuit; an RF input network to feed the rectificationsystem, the RF input network comprising a resistance compression networkthat includes: a first transmission line segment having a firstelectrical length at a first frequency, the first transmission linesegment having an output coupled to the first tuned rectifier circuit; asecond transmission line segment having a second electrical length atthe first frequency, the second electrical length being different fromthe first electrical length, the second transmission line segment havingan output coupled to the second tuned rectifier circuit; and acompression port coupled to inputs of the first and the secondtransmission line segments; wherein, at the first frequency, anequivalent resistance looking into the compression port varies over afirst resistance range as equivalent resistances of the first and secondtuned rectifier circuits vary over a second resistance range, wherein arange ratio of the first resistance range is less than a range ratio ofthe second resistance range, the range ratio comprising a ratio of alargest resistance in a corresponding range to a smallest resistance inthe corresponding range; and a dc-dc converter system having an energyrecovery input port and a dc output port, the energy recovery input portof the dc-dc converter system being coupled to the output port of atleast one tuned rectifier circuit of the rectification system.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features may be more fully understood from the followingdescription of the drawings in which:

FIG. 1 is a block diagram illustrating an exemplary energy recoverysystem in accordance with an embodiment;

FIGS. 2A-2F are schematic diagrams illustrating energy recovery dc-dcconverter systems in accordance with various embodiments;

FIGS. 3A-3F are schematic diagrams illustrating tuned rectifier circuitsthat use diodes to perform rectification in accordance with variousembodiments;

FIGS. 4A-4B are schematic diagrams illustrating tuned rectifier circuitsthat use transistors to perform rectification in accordance with variousembodiments;

FIG. 5 is a schematic diagram illustrating a rectifier circuit having aseries tank and a parallel tank coupled to an input thereof inaccordance with an embodiment;

FIG. 6A is a schematic diagram illustrating an example resistancecompression network (RCN) that may be used to provide power dividing andimpedance shaping at the input of an energy recovery system inaccordance with an embodiment;

FIG. 6B is a schematic diagram illustrating a higher order RCN that maybe used to provide power dividing and impedance shaping at the input ofan energy recovery system in accordance with an embodiment;

FIG. 6C is a schematic diagram illustrating an RCN that utilizestransmission-line sections and reactances to provide power dividing andimpedance shaping at the input of an energy recovery system inaccordance with an embodiment;

FIG. 6D is a schematic diagram illustrating a network that providesun-equal power sharing and impedance shaping at the RF input of anenergy recovery system in accordance with an embodiment;

FIG. 6E is a schematic diagram illustrating a network that may be usedto provide additional power division using an isolating power splitterto divide power among multiple resistance-compressed rectifier systemsin accordance with an embodiment;

FIGS. 7A and 7B are schematic diagrams illustrating conversion networksthat may be used to transfer energy from a floating input voltage portto a common-referenced output port in accordance with embodiments;

FIG. 8A is a schematic diagram illustrating an energy recovery systemusing an isolator as part of the energy recovery system input network inaccordance with an embodiment;

FIG. 8B is a schematic diagram illustrating an energy recovery systemusing a circulator and providing “multilevel” isolation and energyrecovery in accordance with an implementation;

FIG. 9A is a block diagram illustrating an isolator system using energyrecovery at a termination port thereof in accordance with an embodiment;

FIG. 9B is a block diagram illustrating a combiner/splitter using energyrecovery in accordance with an embodiment;

FIG. 9C is a block diagram illustrating a combiner/splitter using energyrecovery that utilizes differential to single-ended conversion in theenergy recovery system in accordance with an embodiment;

FIGS. 9D and 9E are block diagrams illustrating example poweramplification systems using energy recovery in accordance with variousembodiments;

FIG. 10A is a schematic diagram illustrating a transmission-lineresistance compression network (TLRCN) providing power dividing andimpedance shaping and having an input port and two output ports, withthe output ports loaded with a pair of resistive loads;

FIG. 10B is a plot of the normalized input resistance versus thenormalized load resistance for a single-level transmission-lineresistance compression network, with the normalized load resistanceplotted on a log scale;

FIG. 10C is a plot showing the ratio of maximum input resistance tominimum input resistance plotted versus the ratio of maximum loadresistance to minimum load resistance for a single-leveltransmission-line resistance compression network, assuming balancedcompression;

FIG. 10D is a schematic diagram illustrating a transmission-lineresistance compression network (TLRCN) providing power dividing andimpedance shaping and having an input port and two output ports, withthe output ports loaded with a pair of resistive loads;

FIG. 10E is a schematic diagram of an exemplary multi-leveltransmission-line resistance compression network (TLRCN) providing powerdividing and impedance shaping and having an input port and four outputports, with the output ports loaded with resistive loads; and

FIG. 10F is a schematic diagram of an exemplary resistance-compressedrectifier system incorporating a multi-level transmission-lineresistance compression network (TLRCN) and a set of resonant rectifiers.

DETAILED DESCRIPTION

Systems and techniques are described herein for providing desiredoperational characteristics of a resistive termination in a radiofrequency (RF) system, while also allowing power that would normally bedissipated in a resistive termination to be recovered and converted to auseable form. Likewise, a termination to a radio-frequency powerreceiver (such as an antenna or coil) that maintains desirable operatingcharacteristics (e.g., providing a constant matched resistivetermination) as operating conditions change can capture RF power thatwould normally be reflected or lost. To recover RF power and convert itto direct current (dc) signals, the power must be rectified. However,rectification presents many challenges in practice, especially atmicrowave frequencies (e.g., frequencies above 300 MHz).

First, while one may desire a constant resistive input impedance (e.g.,50 Ohms) to realize a desired circuit function, rectifiers at microwavefrequencies typically present effective input impedances that aredifficult to make resistive and which vary with RF power level and dcoutput voltage. In systems having a high peak-to-average power ratio,the problem is particularly challenging. Second, harmonics in the RFinput or associated with the rectifier system itself can affectrectifier behavior, and harmonic voltages or currents generated at theenergy recovery system input by rectifier operation can be problematicto overall system operation. Third, devices capable of rectifieroperation at microwave frequencies are often small (and hence cannotindividually handle needed power levels), and rectifier circuitsemploying them are constrained to operate at low alternating current(ac) input voltages and at dc output voltages that may not be useful forutilizing recovered energy. Moreover, at microwave frequencies, theparasitics associated with rectifier devices (such as, for example,device capacitance and package inductance) can have substantialinfluence on circuit operation, and make it difficult to provide thedesired RF input characteristics. Lastly, the RF input port where theresistor is being replaced is often floating with respect to systemground, while the recovered energy must often be provided at an outputport that is referenced to system ground. In various aspects describedherein, techniques and circuits are provided that make energy recoveryat microwave frequencies practical and effective.

FIG. 1 is a block diagram illustrating an exemplary energy recoverysystem 10 in accordance with an embodiment. As illustrated, the energyrecovery system 10 includes: an energy recovery dc-dc converter system12, a plurality of tuned rectifier circuits 14, and an RF input network16 providing functions such as input impedance shaping, filtering, RFpower distribution to the plurality of rectifier circuits, and/or levelshifting. As will be described in greater detail, in some alternativeembodiments, multiple sets of rectifiers and RF input networks may becoupled to the same energy recovery dc-dc converter. In some otherembodiments, an individual energy recovery dc-dc converter system may beprovided for each rectifier. Other architectures are also possible.

As mentioned above, one challenge to realizing a practical RF energyrecovery system is the fact that effective rectifier input impedance(i.e., the complex ratio of the fundamental component of RF voltage tofundamental RF current at the rectifier input port) depends upon the RFinput power level and the rectifier output voltage. Moreover, the outputvoltage that a practical rectifier device or circuit can operate into isoften not at a useful level for utilizing recovered energy. The energyrecovery dc-dc converter system 12 is provided to address thischallenge.

FIG. 2A is a schematic diagram illustrating an exemplary energy recoverydc-dc converter system 20 in accordance with an embodiment. Asillustrated, the energy recovery dc-dc converter system 20 includes asingle dc-dc converter 22. In some implementations (e.g., designsoperated to include burst-mode operation), input and output capacitancesC_(RO) 24 and C_(OUT) 26 may be provided at the input and output ofconverter 22 to limit voltage ripple under bursting at frequencies belowthe converter switching frequency. The energy recovery dc-dc convertersystem 20 of FIG. 2A may be used in an energy recovery system that uses,for example, a single dc-dc converter (e.g., the energy recovery systemof FIG. 1). As illustrated, converter system 20 includes an input port28 to be coupled to the outputs of the plurality of rectifiers and anoutput port 30 to be coupled to a load network to which recovered energyis to be delivered. In order to provide desired impedancecharacteristics at the RF energy recovery system input, the energyrecovery dc-dc converter system 20 may be controlled to regulate thevoltage at input port 28 while absorbing the power delivered from therectifiers and delivering the absorbed power to output port 30. This canbe achieved using, for example, a dc-dc converter such as a buckconverter, a boost converter, a flyback converter, a buck-boostconverter, or other topology, with control designed to regulate theinput voltage of the dc-dc converter. Output power from the convertercan be provided to a regulated or unregulated output.

The energy recovery system may often be required to operate at highpeak-to-average RF power ratios. Consequently, the instantaneous powerdelivered to the energy recovery dc-dc converter input port 28 may varyover a wide range. Therefore, in some embodiments, converter 22 may beoptimized for operation over a wide range of power levels, including theuse of burst mode, cycle skipping, gate-width switching, phase shedding,and related techniques to maintain high efficiency over a wide powerrange.

In one implementation, the dc-dc converter 22 of FIG. 2A may be ratedfor the peak RF power to be recovered, thereby enabling continuousoperation at peak RF power conditions. In some applications, however, itis known that such peak power conditions only occur for a limitedduration. In these applications, the energy recovery converter inputcapacitor 24 (or other energy storage element) may be made sufficientlylarge such that the converter only needs to process a fraction of thepeak power rating of the recovery system (but at least the average powerrating), while still enabling the voltage at the rectifier output (andthe energy recovery converter input 28) to be regulated to within adesired voltage range.

In many applications, it may be desirable to regulate the energyrecovery converter input 28 to a nearly fixed voltage independent ofrectifier input power, to provide desired operating characteristics (andeffective input impedance values) of the rectifiers and, in turn,desired input impedance characteristics of the energy recovery system.In one exemplary embodiment, this is achieved by comparing the energyrecovery power converter input voltage to a reference voltage togenerate an error signal, and controlling the converter input current,switch current, burst rate, switching frequency, duty ratio or othercontrol variable as a function of the error signal. That is, in thisapproach, the converter input voltage is regulated to a value at or nearthe reference voltage by feedback control of the converter. FIG. 2D is ablock diagram illustrating example circuitry for performing this voltageregulation in accordance with an exemplary embodiment.

Alternatively, the energy recovery converter input voltage V_(RO) may beregulated to a voltage that is a function of the current or powerdelivered to or from the rectifiers. This can be used to extend theoperating power range over which the energy recovery system hasdesirable effective input impedance characteristics (e.g., 50 Ohms,etc.). To understand this, it should be recognized that the effectiveinput resistance of a rectifier is a function of both the power level atwhich the rectifier is operating and of the rectifier output voltage.For example, as is known in the art, some rectifiers ideally provide aninput resistance at the fundamental operating frequency of the formR_(eff)=k(V_(RO))²/P, where R_(eff) is the effective resistance at therectifier input, V_(RO) is the rectifier dc output voltage, P is therectifier output power, and k is a constant that depends on therectifier topology. For an ideal full-bridge diode rectifier topology,for example, k=8/π². For an ideal voltage-doubler rectifier topology,k=2/π² and so on. By adjusting the energy recovery converter inputvoltage (rectifier output voltage) to be smaller for low power (orrectifier current) levels, the effective resistance provided by therectifier can be more approximately constant (vary over a smaller range)than if a constant voltage V_(RO) is used. This can be achieved byadjusting the above-mentioned reference voltage as a function ofmeasured, estimated, or expected power, current or another relatedvariable. It should be noted that to achieve this dynamic referencealternative, it is desirable to size the energy recovery converter inputcapacitance C_(RO) (in conjunction with any rectifier outputcapacitance) large enough such that the rectifier output voltage rippleat the RF frequency and harmonics is small, but small enough that therectifier output voltage can adjust on a time scale associated with thepower variations to be compensated. FIG. 2E is a block diagramillustrating example circuitry for performing voltage regulation with adynamic reference in accordance with an exemplary embodiment.

FIG. 2B is a schematic diagram illustrating an energy recovery dc-dcconverter system 40 in accordance with another embodiment. In thisembodiment, the energy recovery converter 42 is provided with a thirdport 44 from which energy may be drawn and/or delivered. With a thirdport, the energy recovery converter 42 can be configured to regulate thevoltage at both its input port (V_(RO)) 46 and its output port (V_(OUT))48. For example, in one approach, the converter 42 can be configured asa two-input dc-dc converter with a single output. In another approach,the converter 42 can be configured to transfer power in any directionamong the ports 44, 46, 48. Power needed to regulate the output portvoltage that is not sourced from the input port (and rectifiers) caninstead be sourced from the third port 44. Typically, the third port 44will provide an average source of power, but in some cases it may beconstructed as a large energy buffer only, such that long-term averagepower is always sourced from the input port and only temporarily storedat the third port 44. As described above, V_(RO) may be regulated to afixed voltage or to a variable voltage.

FIG. 2C is a schematic diagram illustrating another exemplary energyrecovery dc-dc converter system 50 in accordance with an embodiment. Inthis embodiment, a first converter 52 supplied from a third port 54(V_(P3)) regulates the voltage (V_(RO)) at the energy recovery convertersystem input port 56 (i.e., the rectifier output), while a secondconverter 58 is supplied from this voltage and regulates voltage(V_(OUT)) at an output port 60. While the first and second converters52, 58 may both be provided as switched-mode converters, in someapplications the second converter 58 (regulating V_(OUT)) may berealized as a linear regulator to reduce noise at the output port 60. Insome embodiments, additional converters powered from V_(RO) may beutilized to regulate additional outputs. The additional converters caneach be powered directly from V_(RO) or they can be cascaded so that theoutput of one converter powers the input of another, and so on.

FIG. 2F is a schematic diagram illustrating an energy recovery dc-dcconverter circuit 100 that may be used within an energy recovery systemin accordance with an embodiment. The dc-dc converter circuit 100 usesan off the shelf, integrated, high voltage boost converter IC 102 (e.g.,Texas Instruments TPS61170) that is coupled to control circuitry forsupporting operation in an energy recovery system. The high voltageboost converter IC 102 has a feedback port that was designed for use incontrolling the output voltage of the converter. As shown in FIG. 2F,the energy recovery dc-dc converter circuit 100 includes logic coupledto the feedback port of the boost converter IC 102 that causes the chipto regulate the input voltage of the converter rather than the outputvoltage. It should be appreciated that the energy recovery dc-dcconverter circuit 100 of FIG. 2F is an example of one possible converterdesign that may be used within an energy recovery system in anembodiment. Other converter designs may be used in otherimplementations.

As described previously, one of the functions of the dc-dc convertersystem 12 of FIG. 1 is to convert the dc output signal of therectifier(s) to a useable dc output voltage. As used herein, the phrase“useable dc output voltage” and similar terms refer to voltages that areuseable to perform some desired function. In various implementations,the dc output voltage of the converter may be used to, for example,power other circuitry or devices, charge a battery, provide power to apower amplifier and/or to control circuitry, or perform some otherfunction. In each case, the dc-dc converter system may be used togenerate a dc output voltage that is useable to support thecorresponding function.

As described above, one component in the energy recovery system 10 ofFIG. 1 is the rectifier circuit that converts RF to dc. As shown in FIG.1, in some implementations, a plurality of rectifiers 14 may be used toprovide the overall conversion from RF to dc. A plurality of rectifiersmay be used for multiple reasons. First, devices capable of efficientrectification at microwave frequencies are often small and, therefore,may not be able to handle the needed power levels individually. Second,it is often easier to take advantage of circuit parasitics (or mitigateparasitics) for smaller rectifier devices than for larger ones. Inaddition, as will be described in greater detail, use of a plurality ofrectifiers permits a rectifier system to be constructed that provideslower effective input impedance variation than is provided by a singlerectifier.

In the discussion that follows, the design of individual tuned rectifiercircuits will be described. Techniques for integrating multiplerectifier circuits into a rectification system will be described later.It is desired to have a rectifier that provides approximately resistiveeffective input impedance (i.e., having the fundamental component of RFvoltage substantially in phase with fundamental RF current at therectifier input port) with as little variation in effective impedance(ratio of fundamental voltage to current) as possible across operatingconditions. As is known in the art, the effective impedance presented bya rectifier is a function of power and rectifier output voltage.Moreover, with conventional rectifiers (e.g., implemented with diodes),even the small parasitics associated with device capacitance, packagecapacitance and package inductance can cause substantial deviations fromresistive input impedance. To address these challenges, in at least oneembodiment, rectifiers incorporating tuned networks are used, where thetuned networks incorporate device and/or package parasitics to achievethe desired operating characteristics. Such tuned or resonant rectifierscan provide nearly resistive input resistance characteristics across awide power range (e.g., impedance phase magnitude of less than 20degrees over more than a 5:1 power range, etc.).

FIG. 3A is a schematic diagram of an exemplary tuned rectifier circuit110 in accordance with an embodiment. The tuned rectifier circuit 110 isshown using a Schottky diode 112, but other device types may also beused (e.g., lateral field-effect rectifiers, etc.). Capacitor 114represents a capacitance (C_(R)) including one or more of diodecapacitance, diode package capacitance, and added circuit capacitance,and forms part of the tuning network. Capacitor 116 represents therectifier output capacitance (G_(ROUT)). It provides a low impedance toRF, yielding approximately constant voltage at the rectifier output.Inductor 118 represents the rectifier inductance (L_(R)) which alsoforms part of the tuned network. The value of the rectifier inductance(L_(R)) may include diode package inductance.

In one approach, inductor 118 may be tuned near resonance with capacitor114 (e.g., L_(R) on the order of 1/(4π²f²C_(R))). For a given value ofC_(R), the exact value of L_(R) can be selected using simulationsoftware, such as SPICE. The network is loaded with a specified fixedoutput voltage V_(RO) and driven with a sinusoidal input current i_(RF)(at the design frequency), with L_(R) selected such that the fundamentalof v_(RF) is nearly in phase with i_(RF) for a range of currentamplitudes. One may adjust the value of C_(R) (by changing discretecapacitance, diode size, etc.) and subsequently retune L_(R) in order toachieve resistive operation of the rectifier at a desired range of powerlevels (and to best utilize the rectifier device capabilities). In somecases, to achieve the best resistive input impedance across power, asmall reactance may be added (inductive or capacitive, not shown) inseries with the positive RF input terminal of the rectifier 110. Thisoptional reactance, which would typically be much smaller than thereactance of L_(R) or C_(R), can be used to offset any residualreactance from the tuning process.

FIG. 3B is a schematic diagram illustrating an exemplary tuned rectifiercircuit 120 in accordance with an embodiment. In tuned rectifier 120,C_(ROUT) is again the rectifier output capacitance, which provides a lowimpedance at the operating frequency. C_(R) is the resonant capacitanceand incorporates the diode capacitance, and L_(R) is the resonantinductance and may incorporate diode package inductance. In general,there needs to be a dc current path at the rectifier input. In theembodiment of FIG. 3B, this path is provided by an explicit inductor(i.e., optional choke inductance 122 (L_(DC))) across the inputterminals. In other embodiments, elements external to the rectifier 120may be used to provide the dc current path. Tuning of this rectifier 120may be carried out in a similar manner to the rectifier of FIG. 3A.However, instead of driving the rectifier circuit 120 with a sinusoidalcurrent during tuning, the circuit may be driven with a sinusoidalvoltage while observing the fundamental of the rectifier input current.

In some implementations, rectifier circuits may be provided that alsoinclude tuning for higher-order harmonics. FIG. 3C is a schematicdiagram illustrating such a tuned rectifier circuit 130 in accordancewith an embodiment. As illustrated, the rectifier circuit 130 of FIG. 3Cincludes a series tank 132 having an inductance L2 and a capacitance C2tuned at the second harmonic to reduce device voltage stress. Rectifiercircuits may also be provided that use transmission-line sections toperform some or all of the tuning function. For example, FIG. 3D is aschematic diagram illustrating a tuned rectifier circuit 140 usingtransmission line segments in accordance with an embodiment. Asillustrated, the rectifier circuit 140 of FIG. 3D includes aquarter-wavelength line segment 142 to provide reduced voltage stress.In some implementations, the line length of this segment may be adjustedslightly longer or shorter than a quarter wavelength to compensate forrectifier device capacitance and/or inductance. FIG. 3E is a schematicdiagram illustrating a class E/F rectifier 150 having a differentialinput port 152 in accordance with an embodiment. This rectifier circuit150 can be driven differentially, or its input can be converted to asingle-ended port using a splitter/combiner. It will be appreciated thatother types of tuned rectifier circuit may be used, including those withother harmonic tunings, and those incorporating multiple diodes. Ingeneral, the tuning of a rectifier may involve selecting the inductancesand capacitances such that the ac current (or voltage) at the rectifierinput is substantially in-phase with the ac voltage (or current) at therectifier input for the frequency of interest.

FIG. 3F is a schematic diagram illustrating a resistance compressedrectifier system 160 having a pair of tuned rectifiers preceded by aresistance compression network having a pair of 50 ohm transmission linesegments in accordance with an embodiment. The resistance compressionnetwork acts as an RF input network for the tuned rectifiers (althoughadditional RF input network circuitry may be added in someimplementations). The resistance compressed rectifier system 160 of FIG.3F is operative at 2.14 GHz with a dc output voltage of 7 V and an RFinput impedance near 50 Ohms.

While the tuned rectifier circuits of FIGS. 3A-3F are shown withSchottky diodes, it should be appreciated that other diode types ordevice types may be employed in other implementations to perform therectification function. In some implementations, for example,transistors may be used to provide rectification (e.g., MOSFETs, JFETs,HEMTs, HBTs, etc.). FIG. 4A is a schematic diagram illustrating a tunedrectifier circuit 170 that uses a transistor 172 to performrectification in accordance with an embodiment. As illustrated in FIG.4A, to perform rectification, the gate of the transistor 172 may bebiased to an appropriate dc potential (e.g., V_(B)). Alternatively, thegate terminal may be actively driven at RF to provide synchronousrectification (e.g., V_(B) in FIG. 4A may include a dc bias plus an RFsignal with appropriate phase relative to V_(RF)). FIG. 4B is aschematic diagram illustrating a tuned rectifier circuit 180 thatperforms synchronous rectification using transistors 182, 184 that are“cross-driven” from the RF input signal itself. In general, synchronousrectification involves turning a transistor on and off with timing suchthat it carries an average dc current, thus providing conversion from anac input to a dc output. In one approach, each transistor gate may bedriven such that the transistor conducts current of substantially onepolarity, and is turned off otherwise. That is, the transistor may bedriven to conduct in a manner similar to a diode, but having a lowerdevice drop than a diode.

Another component in the energy recovery system of FIG. 1 is the RFinput network 16 that addresses challenges associated with capturing RFenergy. These challenges include the generation of undesired frequenciesby the rectifiers, the need to operate with small individual rectifierdevices, rectifier input impedance variations, operation at highpeak-to-average power ratios, and energy capture at circuit ports thatare not referenced to a common potential. As will be described below ingreater detail, each of these challenges may be addressed by specificelements of the RF input network.

A byproduct of the rectification process is often the presence of dc,switching harmonics, and other undesired frequency components at therectifier inputs. These undesired frequency components can causedeleterious effects in the energy recovery system. For example, theunwanted frequency content can pollute the system that the energyrecovery system is connected to, can cause undesired interactions amongthe multiple rectifier circuits, as well as other negative effects. Tosuppress this content, filtering may be provided at the rectifier inputsand possibly at points closer to the energy recovery system input. Insome embodiments, these filters may include tuned series and/or paralleltanks in series with the rectifier inputs (and/or interconnections) orin parallel with the rectifier inputs. For example, FIG. 5 is aschematic diagram illustrating a rectifier circuit 190 having a seriestank 192 and a parallel tank 194 coupled to an input thereof, where theseries tank 192 is tuned to the input frequency to pass through thedesired fundamental and the parallel tank 194 is tuned to the inputfrequency to suppress unwanted content. Other bandpass and/or bandstopfiltering (e.g., tuned to harmonics) may also be employed, as well aslow-pass and high-pass filters to suppress undesired content. Thesefilters may be implemented with discrete or integrated passivecomponents, with transmission-line sections, or as a combination ofthese elements.

As described previously, better rectifier performance can sometimes beachieved at RF frequencies using rectifier devices that are small inpower rating and physical size, making it advantageous to construct anenergy recovery system from multiple rectifiers of reduced power rating.Moreover, utilizing a plurality of rectifiers, one can construct arectifier system providing lower effective input impedance variationthan is provided by a single rectifier, as described in detail below. Toimplement a multi-rectifier system, in at least one embodiment, the RFinput network may include a power dividing and impedance shaping networkthat splits power among the various rectifiers and provides an inputimpedance that varies over a smaller range (e.g., a ratio of inputresistances or input impedance magnitudes) than the individualrectifiers. Desirable attributes of such a power dividing networkinclude relatively even power splitting among the individual rectifiersand lossless or very low loss operation.

In some embodiments, a resistance compression network (RCN) may be usedto provide the power dividing and impedance shaping network of the RFinput network. FIG. 6A is a schematic diagram illustrating an exemplaryresistance compression network 200 that may be used in an embodiment.This network is ideally lossless and splits input power among tworectifiers 202, 204 approximately equally, while providing a resistanceat its input port 206 that varies over a smaller range than theindividual rectifiers 202, 204. This thus forms a “resistance-compressedrectifier system.” The compression branch impedance magnitude X isselected based on the input impedance range provided by the rectifiers202, 204. In constructing RCNs of the type in FIG. 6A for operation atmicrowave frequencies, care should be taken to minimize or compensate(e.g., “resonate out”) shunt parasitics at the intermediate nodes (e.g.,between the inductors and capacitors).

The resistance compression network 200 of FIG. 6A, constructed withdiscrete components, has the benefits of being compact and providinggood operational bandwidth. Higher-order resistance compression networks(or “multilevel” compression networks) can also be used, such as the“second order” (or two-level) RCN 210 of FIG. 6B that can split poweramong four rectifier circuits 212, 214, 216, 218. An RCN of order M, oran M-level RCN, can split power among N=2^(M) rectifier circuits. OtherRCN variants may alternatively be used, including RCNs that are achievedby topological duality or star-delta transformations of the networkelements, RCNs that use different component types to realize the neededreactances, and RCNs that use circuit board or microstrip elements.

Power dividing and resistance compression can also be achieved withcircuits incorporating transmission-line sections (e.g., section ofmicrostrip, etc.). FIG. 6C is a schematic diagram illustrating aresistance compression network 230 that uses quarter wavelengthtransmission line sections 236, 238 and reactances 240, 242 to performresistance compression for first and second rectifiers 232, 234. Inresistance compression network 230, the reactive components 240, 242 maybe realized as discrete components, components implemented in thecircuit board, or as transmission-line stubs. In this embodiment, inaddition to working with the shunt elements to realize resistancecompression, the characteristic impedance of the quarter-wave lines 236,238 can be selected to provide a desired degree of impedancetransformation. FIG. 3F described previously illustrates the details ofan example implementation of a resistance-compressed rectifier system160 that uses the resistance compression network architectureillustrated in FIG. 6C.

The power dividing and impedance shaping network of the RF input networkmay also be implemented using other network types and topologies. Forexample, FIG. 6D is a schematic diagram illustrating a network 250 thatserves to provide a degree of impedance shaping such that the impedanceat the RF input 252 varies over a smaller range (e.g., ratio of inputresistances or input impedance magnitudes) than the individualrectifiers 254, 256, though it does not cause power to be shared equallyamong the rectifiers 254, 256 across operating conditions. The network250 can be extended for use with additional rectifiers by parallelingadditional rectifier-loaded quarter-wave-line branches having differentcharacteristic impedances and appropriately designed rectifiers.

Additional power dividing can be obtained using networks that are notideally lossless and/or which do not provide reduction in impedancerange. For example, power may be split further using an isolating powersplitter to divide up power to multiple resistance-compressed rectifiersystems. FIG. 6E illustrates a network 260 that uses a two way splitter262 (e.g., a Wilkinson splitter, a Gysel splitter, a hybrid splitter,etc.) to split power between first and second resistance-compressedrectifier systems 264, 266. Many-way splitters can be used when thereare more than two resistance-compressed rectifier systems. Whileproviding power dividing in this fashion does not provide additionalreduction in impedance ranges, it can be made highly efficient, and theisolation helps soften the variations in input impedance. Moreover, itenables systems of different energy recovery power capacities to besimply constructed.

In some embodiments, the RF input port of an energy recovery system isreferenced to a common potential (e.g., ground, etc.). However, in somecases, the input port may be “differential” or floating (or “flying”)with respect to system ground, while the recovered energy must beprovided at an output port that is referenced to system ground. Forexample, the isolation port of a Wilkinson combiner is not groundreferenced, but represents a “differential” input. One technique torecover energy at a floating or “flying” input port involves the use ofan RF transformer or balun to transfer energy from the flying inputvoltage to a common-referenced port. FIG. 7A is a schematic diagramillustrating an example conversion network 270 for doing this inaccordance with an embodiment. If such an approach is used, the energymay be recovered at the common-referenced port as described above. Inthe embodiment of FIG. 7A, energy at port AB 272 is delivered to outputport CG 274 with V_(CG)=(N₂/N₁)·V_(BA). If the effective turns ratio isnot unity, network 270 also provides an impedance transformation suchthat Z_(diff)=(N₁/N₂)²·Z_(RF). Depending on dc levels, one or both ofthe ports 272, 274 may require a series blocking capacitor, and one mayalso need to tune out transformer parasitics (such as leakageinductances and/or magnetizing inductance) at the RF frequency ofinterest (e.g., using capacitors).

Another technique to transfer energy from a “flying” input port to acommon-referenced port for energy recovery purposes involves the use oftransmission-line sections. FIG. 7B is a schematic diagram illustratingan example conversion network 280 that uses transmission line sections286, 288, 290 to transfer energy between ports in accordance with anembodiment. At the design frequency, conversion network 280 transfersenergy from a floating port 282 to a common-referenced port 284according to the relationship V_(CG)=(Z₀/Z₀)·V_(BA). Network 280 canprovide both a differential to single-ended conversion and an impedancetransformation, such that Z_(diff)=(Z₀/Z₁)²·Z_(RF). In some cases, theZ₁ transmission line section can be omitted. For example, in cases wherethe load provided by the energy recovery system is at or near impedanceZ₁, the transmission section can be omitted. Similarly, in cases wherethe impedance inversion provided by the quarter-wave section 290 is nota problem, this transmission line section can be omitted. Also, it willbe recognized that blocking capacitors may be used in series with one ormore of the terminals of the differential conversion network in someimplementations. Note that the network can also be implemented withlumped transmission-line approximations, with other immittanceconverting circuits taking the function of each quarter-wave section, orcombinations of lumped and distributed structures serving the same orsimilar functions.

Other alternative techniques for converting “flying” or differentialinputs to common-referenced outputs for energy recovery can be utilizedin other embodiments. Combined with the other portions of the energyrecovery system, these techniques enable RF energy to be recovered from“flying” ports.

It is recognized that even with filtering, some applications may besensitive to any reflected power from the energy recovery system(including at the operating frequency, harmonics, or other frequencies).In such cases, an isolator may be used as part of the energy recoveryinput network to terminate any reflected power generated by the energyrecovery system. As shown in FIG. 8A, an isolator 300 may be placed atthe input of an energy recovery block 302 so that reflections from theinput are directed to termination 304. It should be appreciated thatother isolator locations are also possible.

FIG. 8B is a schematic diagram illustrating an energy recovery system310 that uses an isolator 312 to provide “multilevel” isolation andenergy recovery in accordance with an implementation. As shown, a numberof energy recovery blocks 314, 316 are coupled to ports of isolator 312.Each energy recovery block 314, 316 incorporates one or more energyrecovery rectifiers and possibly other subsystems, as described above.Multilevel isolation provides the opportunity to capture RF power atdifferent power levels and contents, and may be implemented with a 4 ormore port circulator and a terminating resistor, or a cascade of 3-portcirculators and a terminating resistor.

The availability of an energy recovery system also enables additionalfunctions and features to be realized. One such function is powermonitoring. For example, an additional circuit can be provided thatmonitors information about the energy recovery system, such as the inputand/or output power of the system. In some implementations, the systemoutput power is monitored using the sensing and/or control signals ofthe energy recovery dc-dc converter. In some other implementations, theoutput power may be monitored using additional low-frequency sensors orother structures. In at least one embodiment, the input power may bemonitored based on the operating point of the rectifier circuits.Alternatively, the input power may be monitored based on the operationof the energy recovery converter (e.g., estimating input power based onthe known characteristics of the system and the converter input oroutput current, voltage, or power or rectifier input or output voltage,current, or power). Additional monitoring circuitry may also be providedin some embodiments. This may include, for example, circuitry formonitoring system temperature, operating status, and/or other criticaloperating parameters.

Many RF circuits incorporate power resistors that dissipate energyduring circuit operation. Such circuits include RF hybrids, powercombiners and dividers, isolators, RF power amplifier systems,duplexers, filters and termination networks, among other devices. Eachof these circuit types can benefit by incorporating the energy recoverytechniques described herein. Likewise, many RF circuits seek to absorbenergy from an antenna, transformer secondary, coil, or other means ofreceiving RF energy, including in rectenna systems, wireless powertransfer systems, inductive power coupling systems, radio-frequencypower converter systems including RF dc-dc converters, and microwavepower transmission systems. It is desirable to be able to capture RFenergy in these systems and convert it to useable form, while minimizingreflected or dissipated RF power. Each of these circuit types canlikewise benefit by incorporating the energy recovery techniquesdescribed herein.

One type of circuit that can benefit from the described techniques is anisolator. FIG. 9A is a block diagram illustrating the use of an energyrecovery system 322 (e.g., the energy recovery system of FIG. 1, etc.)as a termination for an isolator 320. As illustrated, the isolator 320includes a circulator 324 having three ports, with the energy recoverysystem 322 coupled to one of the three ports (i.e., instead of aconventional resistive termination). A first port of the circulatorserves as the input port of the isolator 320 and a second port serves asthe output port. RF power delivered to the isolator input port istransferred to the isolator output port. Any power entering the isolatoroutput port (e.g., power reflected back into the isolator output portfrom a mismatched load and/or any other power) is transferred to theenergy recovery system 322 at the third port of the circulator 324. Inthis manner, the energy may be at least partially recovered for otheruses instead of being lost to dissipation as would occur with aconventional resistive termination.

Another application that can benefit from energy recovery is powercombining and/or splitting. FIG. 9B is a block diagram illustrating theuse of an energy recovery system 330 to provide energy recovery for acombiner/splitter 332 in accordance with an embodiment. Thecombiner/splitter 332 may include, for example, a rat-race hybrid, abranchline hybrid, a 90 or 180 degree hybrid, or others.

In the illustrated embodiment, the combiner/splitter 332 includes fourports: port 1, port 2, a sum port, and a difference (delta) port. Theenergy recovery system 330 may be coupled to either the sum port or thedifference port. The energy recovery system 330 may provide, forexample, a proper termination for the corresponding port (e.g., thedifference port in FIG. 9B) while the other port (e.g., the sum port inFIG. 9B) is used as a “combined” port. In this manner, combining and/orsplitting may be achieved between the combined port and ports 1 and 2,while energy is recovered for isolation at the energy recovery outputport.

In some systems, three (or more) way combining/splitting may be used.FIG. 9C is a block diagram illustrating an implementation that utilizesdifferential to single-ended conversion in an energy recovery system.The combiner/splitter 348 is implemented as a 3-way Wilkinsoncombiner/splitter with the ports for isolation (with energy recovery)connected in delta, where each differential input port has an apparentinput resistance of approximately 3Z₀. This system uses three energyrecovery rectifier systems 340, 342, 344, each includingdifferential-to-single-ended conversion. The system may also include anRF input network comprising impedance shaping, filtering, distribution,and a plurality of rectifiers, along with a single energy recovery dc-dcconverter system 350 to provide recovered energy at the output. In analternative approach, this system can be reconfigured such that there isa separate energy recovery dc-dc converter for each of the energyrecovery systems. This technique may be used for splitting or combiningany number of signals.

Another application that can benefit from the energy recovery techniquesdescribed herein is power amplification. More specifically, systemswhere power from multiple power amplifiers is combined to create asingle higher power signal. FIG. 9D is a block diagram illustrating anexample power amplification system 400 using energy recovery inaccordance with an embodiment. As shown, output power from two poweramplifiers 402, 404 is combined using an isolating combiner 406 withenergy recovery (e.g., as illustrated in FIG. 9B). Depending on therelative magnitude and phase of the outputs of the two power amplifiers402, 404, power will be delivered to one or both of first and secondoutput ports of the combiner 406. The first output port is illustratedas the sum port and the second output port is illustrated as thedifference port in FIG. 9D. An energy recovery system 408 may beconnected to the second output port. This provides the opportunity toload the power amplifiers 402, 404 in an isolating fashion, and at thesame time control power (and signal amplitude and phase) delivered tothe output port by adjusting the magnitudes and phases of the outputs ofthe individual power amplifiers 402, 404. Power not delivered to theoutput port is recovered through the energy recovery system 408 (minusany losses). The magnitudes and phases of the outputs of the individualPAs 402, 404 may be controlled by, for example, any one or more of: (1)individually adjusting one or more of the pulse widths, timing, driveamplitudes, and phases of the power amplifier input signals (e.g.,including amplitude modulation, phase-shift or outphasing modulation,PWM modulation, and on/off modulation), (2) individually adjusting thepower supply bias voltages of the power amplifiers (e.g., via discreteor continuous drain modulation), (3) load modulation of the individualpower amplifiers (e.g., by implementing each power amplifier as aDoherty amplifier or an outphasing amplifier with lossless combining),and/or other techniques. It should be recognized that such a system canalso be realized with a larger number of power amplifiers, such as byusing the combining and energy recovery system illustrated in FIG. 9C.Such a system enables high efficiency linear control of output power byadjusting the relative operation of the individual power amplifiers.

A power amplifier system with multiple power amplifiers can also beimplemented as a balanced power amplifier system that realizes improvedefficiency under load mismatch (e.g., from a non-ideal load impedance)at its output port. FIG. 9E is a block diagram illustrating an exemplarysystem 420 of this type. In system 420, reflected power from an outputport of a balanced amplifier 422 is captured by an energy recoverysystem 424. The recovered energy is provided at a dc output port 426 andmay be used to supply part of the power to the power amplifiers 428, 430of balanced amplifier 422, for powering computation or controlcircuitry, powering pre-amplifiers, and/or for other uses. The system420 of FIG. 9E includes a first 90-degree hybrid 440 to provideappropriate phases at the two power amplifier inputs, and a second90-degree hybrid 442 to combine power from the two power amplifiers 428,430 for delivery to an RF output port. The energy recovery system 424 isconnected to the isolation port of the second hybrid 442. Reflectedpower entering the output port (e.g., owing to load mismatch) can besubstantially captured by the energy recovery system 424, thus providingimproved operation under load mismatch.

Resistance compression networks (RCNs) absorb energy from a source anddeliver it (ideally losslessly) to a plurality of loads (e.g., such aset of rectifiers), providing an input resistance that varies over anarrow range as the resistance of the loads vary together over a widerange. Resistance compression networks can also serve to reduce thephase of the input impedance as compared to the phase of the loadimpedances (phase compression). Ideally, the RCN splits input powersubstantially equally among the loads. Conventional resistancecompression networks use reactances to accomplish this, and mayadditionally include transmission-line sections, as illustrated in FIGS.3F and 6C. The reactances themselves may be implemented astransmission-line sections or stubs or otherwise realized inprinted-circuit form.

In some embodiments, resistance compression networks may be implementedusing transmission-line sections having asymmetric lengths, wherein thetransmission-line sections are provided as two-port structuresinterconnecting among the source and loads. Such Transmission-LineResistance Compression Network (TLRCN) implementations may provideseveral benefits. For example, they can (a) have low loss, (b) enablerepeatable, low-cost implementation using printed circuit techniques,(c) provide filtering, and (d) with correct length selections, they canprovide resistance compression at one or more harmonic frequencies.Moreover, at UHF frequencies and above, the discrete reactances oftenused in conventional RCN designs represent an increasing challenge. Thatis, the transmission-line effects associated with their physical sizecan substantially influence system behavior, and their numerical valuescan become extremely small, making them difficult to implementaccurately and making the system susceptible to parasitic effects. TLRCNimplementations, on the other hand, avoid these issues by directlyrealizing the RCN as a transmission-line structure interconnecting thesource and loads.

A description will now be made of the theory and operatingcharacteristics of Transmission-Line Resistance Compression Networks.With a TLRCN network, substantially balanced splitting of power tomultiple loads and smaller variation in driving point resistance ascompared to load resistance variation may be achieved using onlytransmission-line sections used as two-port devices to connect among thesources and loads. FIG. 10A shows a basic TLRCN structure, having asingle input port (or compression port) with voltage v_(IN) and twooutput ports with voltages v_(O1) and v_(O2), with the output portsloaded with identical resistive loads R_(L). In each transmission-linesection, or branch, in FIG. 10A the second terminal at each port of eachtransmission-line section may be treated as connected to a commonpotential at that end of the transmission-line section, as naturallyoccurs in a microstrip or other printed-circuit implementation, and isthus not shown explicitly. The first transmission-line branch 500coupled to the input port has characteristic impedance Z₀ and a lengthl₁ corresponding to an electrical angular delay θ₁ at an operatingfrequency of interest. The second transmission-line branch 502 coupledto the input port likewise has characteristic impedance Z₀ and adifferent length l₂ corresponding to an electrical angular delay θ₂.(Implementation of systems in which the two branches have differentcharacteristic impedances and which operate best with different loadingimpedances is also possible.) We can express the lengths of the twobranches as a base length plus and minus a delta length (or a base angle+/−a delta angle) as follows:

l ₁ =l _(Base) +Δl

l ₂ =l _(Base) −Δl  (1)

θ₁=θ_(Base)+Δθ

θ₂=θ_(Base)−Δθ  (2)

We obtain desired operating characteristics at a frequency of interestby proper selection of Z₀, θ_(Base), and Δθ.

While there are multiple possibilities for base lengths, we firstconsider a base length l_(Base) of λ/4 (a quarter wavelength at afrequency of interest), corresponding to θ_(Base)=π/2 radians. (Any baselength with an additional multiple of λ/2 in length will provide similarresults.) Considering the first and second branches 500, 502 in FIG. 10Aindividually, we find branch input admittances at the frequency ofinterest:

$\begin{matrix}{{Y_{{in},1} = {\frac{1}{Z_{{in},1}} = {\frac{1}{Z_{0}} \cdot \frac{Z_{0} - {j\; R_{L}{\cot \left( {\Delta \; \theta} \right)}}}{R_{L} - {j\mspace{11mu} Z_{0}{\cot \left( {\Delta \; \theta} \right)}}}}}}{Y_{{in},2} = {\frac{1}{Z_{{in},1}} = {\frac{1}{Z_{0}} \cdot \frac{Z_{0} + {j\; R_{L}{\cot \left( {\Delta \; \theta} \right)}}}{R_{L} + {j\; Z_{0}{\cot \left( {\Delta \; \theta} \right)}}}}}}} & (3)\end{matrix}$

Since these admittances are complex conjugates, the network will dividepower entering the input port equally to both loads (for identical loadresistances). The impedance seen at the input port at the frequency ofinterest is resistive in this case, and can be shown to be:

$\begin{matrix}{Z_{in} = {R_{in} = {\frac{{\cot \left( {\Delta \; \theta} \right)}}{2\left\lbrack {1 + {\cot^{2}\left( {\Delta \; \theta} \right)}} \right\rbrack} \cdot \left\lbrack {\left\{ \frac{R_{L}}{{\cot \left( {\Delta \; \theta} \right)}} \right\} + \frac{Z_{0}^{2}}{\left\{ \frac{R_{L}}{{\cot ({\Delta\theta})}} \right\}}} \right\rbrack}}} & (4)\end{matrix}$

Such a characteristic clearly realizes resistance compression: the inputimpedance is resistive and varies only over a small range as the loadresistances vary together over a wide range. In fact, this inputresistance characteristic bears close relation to the input resistanceof a type of resistance compression network that uses reactances inseries with the load networks (e.g., see FIG. 6A). With a designselection of Δθ=π/4 radians (Δl=λ/8), the circuit provides identicalcharacteristics (with the transmission-line characteristic impedance Z₀taking the place of reactance X in the expression for the inputresistance).

In general, a resistance range looking into a resistance compressionnetwork described herein will be less than the resistance rangeassociated with the corresponding loads. More specifically, a “rangeratio” looking into the resistance compression network will be less thanrange ratios associated with the loads, where the range ratio of aresistance range is defined as the ratio of a largest resistance valuein the range to a smallest resistance value in the range.

Using the above-described network with a base angle of θ_(Base)=π/2,“balanced” compression can be achieved for a range of load resistanceshaving a geometric mean of R_(L,center):

R _(L,center) =Z ₀·|cot(Δθ)|  (5)

At this load resistance value (R_(L,center)), the input resistance takeson a minimum value of R_(in,min), with larger input resistance for otherload resistances. The value of R_(in,min) may be calculated as follows:

$\begin{matrix}{R_{{in},\min} = {Z_{0} \cdot \frac{{\cot ({\Delta\theta})}}{\left\lbrack {1 + {\cot^{2}({\Delta\theta})}} \right\rbrack}}} & (6)\end{matrix}$

FIG. 10B shows a plot of the input resistance (normalized to R_(in,min))as a function of the load resistance (normalized to R_(L,center)), withthe normalized load resistance on a log scale. FIG. 10C shows the detailof the ratio of the maximum to minimum input resistance plotted as afunction of the maximum to minimum load resistance, assuming balancedcompression (i.e., with R_(L,center) selected as the geometric mean ofR_(L,max) and R_(L,min)). For this case, we find:

$\begin{matrix}{\frac{R_{{in},\max}}{R_{{in},\min}} = {\frac{1}{2}\left\lbrack {\sqrt{\frac{R_{L,\max}}{R_{L,\min}}} + \sqrt{\frac{R_{L,\min}}{R_{L,\max}}}} \right\rbrack}} & (7)\end{matrix}$

Which, for large values of R_(L,max)/R_(L,min) approaches:

$\begin{matrix}{\frac{R_{{in},\max}}{R_{{in},\min}} \approx {\frac{1}{2}\sqrt{\frac{R_{L,\max}}{R_{L,\min}}}}} & (8)\end{matrix}$

The high degree of resistance compression provided by this system can beseen in these expressions and in FIG. 10C, with a 10:1 ratio of loadresistance compressed to a 1.74:1 ratio in input resistance and a 100:1ratio in load resistance compressed to only a 5.05:1 ratio in inputresistance. As with conventional resistance compression networks, onecan also use the TLRCN to provide phase compression in which foridentical non-resistive loads, the input impedance is more nearlyresistive than the load impedances themselves.

It should be noted that other base lengths besides l_(Base)=λ/4(θ_(Base)=π/2 radians) can be used. For example, a base length ofl_(Base)=λ/2 (θ_(Base)=π radians) likewise results in equal powertransfer to the two loads and a compressed resistive input impedance.The characteristics associated with this base length will be the same asthat in Equations (3)-(6), except with cot(Δθ) replaced with −tan(Δθ) ineach expression. Likewise, operation will be the same with anyadditional multiple of λ/2 added to the base length. Because of this,with appropriate selections of base length at a desired fundamentalfrequency, the system can be designed to also provide resistancecompression at one or more harmonic frequencies (and at subharmonicfrequencies), provided that the loads have appropriate frequencycharacteristics.

There are multiple possible design approaches for TLRCN circuits.Considering a base length l_(Base)=λ/4 (θ_(Base)=π/2 radians), one may apriori select a value of Δθ=π/4 radians (Δl=λ/8), such that θ₁=3π/4 andθ₂=π/4. For balanced compression, one may then select Z₀ as R_(L,center)(the geometric mean of the maximum and minimum load resistancesR_(L,max) and R_(L,min)). In this case, the load resistances loadingeach transmission-line section vary (geometrically) about thecharacteristic impedance of the lines, which helps reduce requiredtransmission-line reflection and loss. This design choice provides acompressed input resistance having a range of values determined by theload resistances. In cases where this range of input resistance valuesis not what is desired for the system, an additional impedancetransformation stage may be placed at the input of the TLRCN. One highlyeffective means to do this is to add an additional quarter-wave line atthe input to the compression stage (referred to herein as thecompression port), as illustrated in FIG. 10D.

The whole transmission-line structure of FIG. 10D is likewise itself aresistance compression network having both a compression stage and atransformation stage. The quarter wave line is selected to have acharacteristic impedance Z_(T) that provides an impedance transformationbetween the resistance obtained at the input of the compression stage(e.g., Z_(in,median), the median of the range of the input resistanceZ_(in) or a similar value related to Z_(in)) and that desired for theinput of the system (Z_(in,T)). In this case, to obtain an overall inputresistance near a desired value Z_(in,T,desired), we may select:

Z _(T)=√{square root over (Z _(in,T,desired) ·Z _(in,median))}.  (9)

Another design approach takes advantage of the freedom to choose boththe differential length and the characteristic impedance of thetransmission lines. One can also choose the base length. In the examplethat follows, a base length of θ_(Base)=π/2 radians at the operatingfrequency will be used. By properly selecting the differential lengthand the characteristic impedance, within certain bounds, one candirectly realize both resistance compression and a desired specifiedinput resistance directly with the structure of FIG. 10A. In this designapproach, one may start with a center resistance R_(L,center) aboutwhich load resistances are compressed. For balanced compression,R_(L,center) is chosen as the geometric mean of the maximum and minimumload resistances, R_(L,max) and R_(L,min). A desired minimum inputresistance R_(in,min) of any value below R_(L,center) may then bechosen. The input resistance will take on values at and aboveR_(in,min), with the range of R_(in) values depending on the range ofthe R_(L) values as per Equation (7). One option is to select R_(in,min)to be the desired resistance R_(in,desired) seen at the input of theTLRCN (recognizing that the actual input resistance will be at or abovethe desired value). Another option is to set the median value of theinput resistance that occurs over the range of load resistances to matchthe desired input resistance. To achieve this for a given maximum tominimum load resistance ratio, one may select R_(in,min) as follows:

$\begin{matrix}{R_{{in},\min} = \frac{2 \cdot R_{{in},{desired}}}{1 + {\frac{1}{2}\sqrt{\frac{R_{L,\max}}{R_{L,\min}}}} + {\frac{1}{2}\sqrt{\frac{R_{L,\min}}{R_{L,\max}}}}}} & (10)\end{matrix}$

One could likewise select R_(in,min) to be some other value close toR_(in,desired) to achieve good results.

Based on selecting R_(L,center) and R_(in,min) as described above (withresistance R_(in,min) necessarily selected below R_(L,center)), one candirectly choose Z₀ and Δθ of the network of FIG. 10A to provide both theneeded compression and impedance transformation, as follows:

$\begin{matrix}{{\cot ({\Delta\theta})} = \sqrt{\frac{R_{L,{center}}}{R_{{in},\min}} - 1}} & (11) \\{Z_{0} = \frac{R_{L,{center}}}{\sqrt{\frac{R_{L,{center}}}{R_{{in},\min}} - 1}}} & (10)\end{matrix}$

This design choice has the advantage of providing both resistancecompression and impedance transformation (where needed) in a compactstructure. However, the practicality of such an implementation willdepend on the desired values. For example, as R_(in,min) approachesR_(L,center), the characteristic impedance of the transmission line cangrow unreasonably large. It should also be appreciated that one can usethe selection of the transmission-line impedance and differential lengthto provide a first-degree of impedance transformation, and add anotherquarter-wave transformer at the input (and/or a set of quarter-wavetransformers between the base compression stage and the loads) toprovide additional impedance transformation.

As with conventional resistance compression networks, one may constructmulti-stage or multi-level compression networks to provide greaterdegrees of resistance compression than obtained with a single-leveldesign. As with conventional resistance compression networks, this maybe done by cascading single-level resistance compression stages in atree structure (e.g., a binary tree, etc.), though other structuralimplementations of multi-level TLRCNs are possible. FIG. 10E shows anexemplary two-stage TLRCN. This example utilizes l_(Base)=λ/4(θ_(Base)=π/2 radians), and differential lengths Δl=λ/8 (Δθ=π/4) radians(Δl=λ/8), such that θ₁=3π/4 and θ₂=π/4 in each stage. With thisselection of differential lengths, a multi-stage TLRCN can be optimized(in terms of minimizing the peak deviation from a median inputresistance) just as with conventional reactance-based multi-level RCNs(see, e.g., “A New Power Combining and Outphasing Modulation System forHigh-Efficiency Power Amplification,” by Perreault et al., IEEETransactions on Circuits and Systems—I, Vol. 58, No. 8, pp. 1713-1726,August 2011; and U.S. Patent Publication No. 2011/0187437 to Perreaultet al., entitled “Radio-Frequency (RF) Amplifier Circuits and RelatedTechniques,” which is hereby incorporated by reference in its entirety),with the transmission-line characteristic impedances of the lines in thetwo stages taking the place of the reactance amplitudes of the twostages. Alternatively, both the characteristic impedances and the baseand differential lengths of each stage can be optimized to provide anoverall desired input resistance level and transformation, with theopportunity to achieve additional goals through the parameter selection,such as minimizing RCN loss. Although illustrated with two stages inFIG. 10E, it should be appreciated that additional stages may be addedto provide further resistance compression.

Combining a transmission-line resistance compression network with a setof rectifiers forms a resistance compressed rectifier system. Anexemplary resistance-compressed rectifier system 520 incorporating aTLRCN is shown in FIG. 10F. This system is for 2.14 GHz operation, andhas four tuned rectifiers as loads for the TLRCN that act asapproximately resistive loads, each providing ac input impedance of˜24-160Ω over an input power range of 0.125-1.07 W (and a dc rectifieroutput power of 0.08-0.85 W) at a rectifier output voltage of 7 V. Therectifier also includes a series-resonant input filter, and is tuned forresistive operation by appropriate resonance between the devicecapacitance and output inductance. Note that these filtering and tuningelements can be provided as discrete components or constructed in aprinted circuit board (optionally including elements such astransmission-line sections, gap capacitors, etc.). The TLRCN has twocompression stages and a transformation stage. The firstcompression-stage “A” compresses the resistances presented by therectifiers into a range of 31-46Ω (for the first-stage input impedancesZ_(in,A1) and Z_(in,A2), which act as the load for the second stage ofcompression). The second stage further compresses this to an inputimpedance Z_(in,B) of approximately 19-19.4Ω resistive over therectifier load resistance range. The transformation stage, comprising aquarter-wave line, transforms this impedance into the overall inputimpedance of approximately 50Ω.

It will be appreciated that the inventive energy recovery system can beemployed in numerous other applications in which energy isconventionally delivered to a resistive termination. By replacing thelossy termination with the energy recovery system, the power that wouldotherwise be lost can be captured and converted to a useful form, whilemaintaining a desirable loading characteristic at the termination port.

Having described exemplary embodiments of the invention, it will nowbecome apparent to one of ordinary skill in the art that otherembodiments incorporating their concepts may also be used. Theembodiments contained herein should not be limited to disclosedembodiments but rather should be limited only by the spirit and scope ofthe appended claims. All publications and references cited herein areexpressly incorporated herein by reference in their entirety.

What is claimed is:
 1. A circuit comprising: first and second loadshaving substantially the same input impedances under substantially thesame operating conditions; and a transmission-line resistancecompression network, including: an input port; a first output portcoupled to the first load; a second output port coupled to the secondload; and a transmission-line network coupled to the input port, thefirst output port, and the second output port, the transmission-linenetwork comprising at least two transmission lines of different lengths;wherein, for a first operating range, the resistances at input ports ofthe first and second loads vary over first and second ratios,respectively, the resistance of the input impedance at the input port ofthe transmission-line compression network varies over a third ratio, andthe third ratio is smaller than at least one of the first and secondratios.
 2. The circuit of claim 1, wherein: the transmission-lineresistance compression network is configured to provide substantiallybalanced splitting of power between the first and second output ports.3. The circuit of claim 1, wherein: the transmission-line resistancecompression network is substantially lossless.
 4. The circuit of claim1, wherein the transmission-line resistance compression networkcomprises: a first transmission line having an input and an output, thefirst transmission line having a length that is a multiple of a quarterwavelength plus a first additional length at a first operatingfrequency, wherein the output of the first transmission line is coupledto the first output port of the transmission-line resistance compressionnetwork; and a second transmission line having an input and an output,the second transmission line having a length that is a multiple of aquarter wavelength minus the first additional length at the firstoperating frequency, wherein the output of the second transmission lineis coupled to the second output port of the transmission-line resistancecompression network; wherein the input of the first transmission lineand the input of the second transmission line are coupled together toform a port.
 5. The circuit of claim 1, wherein: the first and secondloads include rectifier circuits.
 6. The circuit of claim 1, wherein:the transmission-line resistance compression network is an M-stagenetwork connected to 2^(M) loads and comprising 2^(M) transmission-linesections incorporating transmission lines of at least two differentlengths, where M is an integer greater than one.
 7. The circuit of claim6, wherein: the transmission-line resistance compression networkcomprises a binary tree of transmission-line sections.
 8. A method forcompressing resistances associated with a plurality of loads, the methodcomprising: transforming an input impedance of a first load using afirst transmission line segment having a first electrical length at afirst frequency, the first load being associated with a first resistancerange at the first frequency; transforming an input impedance of asecond load using a second transmission line segment having a secondelectrical length at the first frequency, the second load beingassociated with a second resistance range at the first frequency; andproviding a compressed resistance range at a compression port that iscoupled to inputs of the first and second transmission line segments atthe first frequency, the compressed resistance range having a rangeratio that is less than a range ratio associated with at least one ofthe first resistance range and the second resistance range, wherein arange ratio of a range comprises a ratio between a highest value in therange and a lowest value in the range.
 9. The method of claim 8,wherein: the first and second loads have input impedances that vary insubstantially the same manner under similar conditions.
 10. The methodof claim 8, wherein: the first and second transmission line segmentseach have substantially the same characteristic impedance Z₀.
 11. Themethod of claim 10, wherein: the first transmission line segment has anelectrical length of π/2+Nπ+Δθ radians and the second transmission linesegment has an electrical length of π/2+Mπ−Δθ radians, where N,Mε[0, 1,2, . . . ].
 12. The method of claim 11, wherein: the resistance range ofthe first and second loads at the first frequency has a lower boundR_(L,min), an upper bound R_(L,max), and a center value R_(L,center)that is the geometric mean of R_(L,min) and R_(L,max); and thecharacteristic impedance Z₀ of the first and second transmission linesegments is approximately:Z ₀ =R _(L,CENTER)/|cot(Δθ)|.
 13. The method of claim 10, wherein: thefirst transmission line segment has an electrical length of π+Nπ+Δθradians and the second transmission line segment has an electricallength of π+Mπ−Δθ radians, where N,Mε[0, 1, 2, . . . ].
 14. The methodof claim 13, wherein: the resistance range of the first and second loadsat the first frequency has a lower bound R_(L,min), an upper boundR_(L,max), and a center value R_(L,center) that is the geometric mean ofR_(L,min) and R_(L,max); and the characteristic impedance Z₀ of thefirst and second transmission line segments is approximately:Z ₀ =R _(L,CENTER)/|tan(Δθ)|.
 15. The method of claim 8, wherein: thefirst and second loads include rectifier circuits.
 16. The method ofclaim 8, further comprising: transforming the resistance at thecompression port using a third transmission line segment having anelectrical length of one quarter wavelength at the first frequency. 17.An energy recovery system to simulate behavior of a resistivetermination for a radio frequency (RF) circuit coupled to the energyrecovery system, the energy recovery system comprising: a rectificationsystem having a plurality of tuned rectifier circuits, the plurality oftuned rectifier circuits including at least a first tuned rectifiercircuit and a second tuned rectifier circuit; an RF input network tofeed the rectification system, the RF input network comprising aresistance compression network that includes: a first transmission linesegment having a first electrical length at a first frequency, the firsttransmission line segment having an output coupled to the first tunedrectifier circuit; a second transmission line segment having a secondelectrical length at the first frequency, the second electrical lengthbeing different from the first electrical length, the secondtransmission line segment having an output coupled to the second tunedrectifier circuit; and a compression port coupled to inputs of the firstand the second transmission line segments; wherein, at the firstfrequency, an equivalent resistance looking into the compression portvaries over a first resistance range as equivalent resistances of thefirst and second tuned rectifier circuits vary over a second resistancerange, wherein a range ratio of the first resistance range is less thana range ratio of the second resistance range, the range ratio comprisinga ratio of a largest resistance in a corresponding range to a smallestresistance in the corresponding range; and a dc-dc converter systemhaving an energy recovery input port and a dc output port, the energyrecovery input port of the dc-dc converter system being coupled to theoutput port of at least one tuned rectifier circuit of the rectificationsystem.
 18. The energy recovery system of claim 17, wherein: thecompression port is a first compression port; the plurality of tunedrectifier circuits further includes at least a third tuned rectifiercircuit and a fourth tuned rectifier circuit; and the resistancecompression network further comprises: a third transmission line segmenthaving a third electrical length at the first frequency, the thirdtransmission line segment having an output coupled to the third tunedrectifier circuit; a fourth transmission line segment having a fourthelectrical length at the first frequency, the fourth electrical lengthbeing different from the third electrical length, the fourthtransmission line segment having an output coupled to the fourth tunedrectifier circuit; and a second compression port coupled to inputs ofthe third and fourth transmission line segments; wherein, at the firstfrequency, an equivalent resistance looking into the second compressionport varies over a third resistance range as equivalent resistances ofthe third and fourth tuned rectifier circuits vary over a fourthresistance range, wherein a range ratio of the third resistance range isless than a range ratio of the fourth resistance range.
 19. The energyrecovery system of claim 18, wherein the resistance compression networkfurther comprises: a fifth transmission line segment having a fifthelectrical length at the first frequency, the fifth transmission linesegment having an output coupled to the first compression port; a sixthtransmission line segment having a sixth electrical length at the firstfrequency, the sixth electrical length being different from the fifthelectrical length, the sixth transmission line segment having an outputcoupled to the second compression port; and a third compression portcoupled to inputs of the fifth and sixth transmission line segments;wherein, at the first frequency, an equivalent resistance looking intothe third compression port varies over a fifth resistance range asequivalent resistances at the first and second compression ports varyover first and third resistance ranges, respectively, wherein a rangeratio associated with the fifth resistance range is less than rangeratios associated with the first and third resistance ranges.
 20. Theenergy recovery system of claim 19, wherein the first and thirdresistance ranges are substantially the same.